Question

A bag contains $4$white, $5$black, and $6$red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

• A. $\frac{4}{15}$
• B. $\frac{1}{2}$
• C. $\frac{2}{5}$
• D. $\frac{2}{3}$

Answer 1

The correct option is D

$\frac{2}{3}$

The explanation for the correct answer:

Step 1: Express the given data:

Number of white balls = $4$

Number of black balls = $5$

Number of red balls = $6$

Total number of balls $=4+5+6$

$=15$

Step 2: Finding the probability:

Probability of getting a white ball = $\frac{4}{15}$

Probability of getting a red ball = $\frac{6}{15}$

The probability that the drawn ball is either white or red

$$\begin{gathered} =\frac{4}{15}+\frac{6}{15} \\ =\frac{10}{15} \\ =\frac{2}{3} \end{gathered}$$

Hence, option (D) is the correct answer.